Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024

in my iteration is appear Error, (in assuming) when calling 'evala/preproc4'. Received: 'floats not handled' which i know is  becuase assuming but how fix it?

and how i can get that table ?

error-problem.mw

i want plot like that but i can't  and there is anyway for finding the equalibriom point of system? 

restart

with(PDEtools)

with(LinearAlgebra)

with(DEtools)

with(DynamicSystems)

sys := {diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

{diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)}

(1)

fns := {x(t), y(t)}

{x(t), y(t)}

(2)

sol := dsolve(sys, fns)

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

(3)

ode := [diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]; S := dsolve(ode)

[diff(x(t), t) = 2*x(t)+3*y(t), diff(y(t), t) = 2*x(t)+y(t)]

 

{x(t) = c__1*exp(4*t)+c__2*exp(-t), y(t) = (2/3)*c__1*exp(4*t)-c__2*exp(-t)}

(4)

Student:-ODEs:-ODESteps(ode, {x(t), y(t)})

"[[,,"Let's solve"],[,,[(ⅆ)/(ⅆt) x(t)=2 x(t)+3 y(t),(ⅆ)/(ⅆt) y(t)=2 x(t)+y(t)]],["•",,"Define vector"],[,,x(t)=[?]],["•",,"Convert system into a vector equation"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)+[?]],["•",,"System to solve"],[,,(ⅆ)/(ⅆt) x(t)=[?]*x(t)],["•",,"Define the coefficient matrix"],[,,A=[?]],["•",,"Rewrite the system as"],[,,(ⅆ)/(ⅆt) x(t)=A*x(t)],["•",,"To solve the system, find the eigenvalues and eigenvectors of" A],["•",,"Eigenpairs of" A],[,,[[-1,[?]],[4,[?]]]],["•",,"Consider eigenpair"],[,,[-1,RTABLE(18446744074191517278,MATRIX([[-1], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[1]=[]],["•",,"Consider eigenpair"],[,,[4,RTABLE(18446744074192645174,MATRIX([[3/2], [1]]),Vector[column])]],["•",,"Solution to homogeneous system from eigenpair"],[,,(x)[2]=[]],["•",,"General solution to the system of ODEs"],[,,x=`c__1` (x)[1]+`c__2` (x)[2]],["•",,"Substitute solutions into the general solution"],[,,x=[]+[]],["•",,"Substitute in vector of dependent variables"],[,,[?]=[?]],["•",,"Solution to the system of ODEs"],[,,{x(t)=-`c__1` (e)^(-t)+(3 `c__2` (e)^(4 t))/2,y(t)=`c__1` (e)^(-t)+`c__2` (e)^(4 t)}]]"

(5)
 

NULL

Download Plot-1.mw

Hi,

I’m not very familiar with how to handle complex numbers in Maple, but I’d like to solve a final exam exercise (June 2025) on complex numbers in this environment. I’ve already solved it using pen and paper. My goal is also to illustrate the different results graphically, for pedagogical purposes, so I’d like some guidance to translate my pen-and-paper solution.

Bac_25_SM_Complexes.mw

Epreuve_Bac_SM_2025_Ss1_Sol-Exo-02.pdf

we have a lot term which we add thus term we can get something near to our solution but i don't know how it is work , did any one did pade approximate of series solution?

restart

with(inttrans)

with(PDEtools)

with(DEtools)

with(Physics)

declare(u(x, t), quiet); declare(v(x, t), quiet); declare(U(x, t), quiet)

undeclare(prime)

approx_sol := -8*x + 3 - 208/3*x^3 + 24*x^2 + 2279/15*x^5 + 200*x^4 + 443/63*x^7 + 676/15*x^6 + 62/2835*x^9 + 62/105*x^8

-8*x+3-(208/3)*x^3+24*x^2+(2279/15)*x^5+200*x^4+(443/63)*x^7+(676/15)*x^6+(62/2835)*x^9+(62/105)*x^8

(1)
 

NULL

Download pade-approximate.mw

in this substitution really is hard to substitute which i don't have idea how find u[1]  u[2] so on becuase  in that term some function like u[i,x] appear and i don't have idea how define them to remove it in my iteration ? and how remove the conjugate of function u[0] i did try evalc(u[0]) and make it worst than this 

which i did some special substitution which i don't know true or not but result is true i didn't have other idea for that
which  instead of any conjugate i use v and istead of any diff(u,x) i use z[i,x] and if conjugate have derivative v[i,x]

k4.mw

is easy to determine the linear and non linear part but how we can do it by command specially when contain conjugate part of function even i try to use another function instead of conjugate but stil i didn't got  the result?

restart

with(inttrans)

with(PDEtools)

with(DEtools)

with(DifferentialAlgebra)

"with(Student[ODEs][Solve]): "

with(IntegrationTools)

with(inttrans)

with(PDEtools)

with(Physics)

with(PolynomialTools)

with(RootFinding)

with(SolveTools)

with(LinearAlgebra)

with(sumtools)

declare(u(x, t))*conjugate(u(x, t))*declare(v(x, t))

u(x, t)*`will now be displayed as`*u

 

v(x, t)*`will now be displayed as`*v

 

conjugate(u(x, t))

(1)

pde := u(x, t)+I*(diff(u(x, t), `$`(x, 2)))+2*(diff(u(x, t)*conjugate(u(x, t)), x))*u(x, t)+u(x, t)^2*conjugate(u(x, t))^2*u(x, t) = 0

u(x, t)+I*(diff(diff(u(x, t), x), x))+2*((diff(u(x, t), x))*conjugate(u(x, t))+u(x, t)*(diff(conjugate(u(x, t)), x)))*u(x, t)+u(x, t)^3*conjugate(u(x, t))^2 = 0

(2)

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, t) = T*u(x, t)))/T, T) end proc, expand(pde))

() = 0, u(x, t)+I*(diff(diff(u(x, t), x), x))+2*u(x, t)*(diff(u(x, t), x))*conjugate(u(x, t))+2*u(x, t)^2*(diff(conjugate(u(x, t)), x))+u(x, t)^3*conjugate(u(x, t))^2 = ()

(3)

u_occurrences := map(proc (i) options operator, arrow; numelems(select(has, [op([op(i)])], u)) end proc, oppde); linear_op_indices := ListTools:-SearchAll(1, u_occurrences); pde_linear := add(oppde[[linear_op_indices]]); pde_nonlinear := expand(simplify(expand(pde)-pde_linear))

Error, invalid input: ListTools:-SearchAll expects its 2nd argument, L, to be of type {list, rtable}, but received 0

 

[linear_op_indices]

 

Error, (in simpl/relopsum) invalid terms in sum: u(x,t)+I*diff(diff(u(x,t),x),x)+2*u(x,t)*diff(u(x,t),x)*conjugate(u(x,t))+2*u(x,t)^2*diff(conjugate(u(x,t)),x)+u(x,t)^3*conjugate(u(x,t))^2 = 0

 
 

NULL

Download solving.mw

I am trying to check if a matrix quailfies as being skew-symmetric. So I added it to it's transpose to get a matrix of zeroes. 

How do I check it  equals the ZeroMatrix?

restart

NULL

M := Matrix(3, 3, {(1, 1) = 0, (1, 2) = (40*sqrt(7)+140)/(560+sqrt(7)), (1, 3) = (80*sqrt(7)+35)/(560+sqrt(7)), (2, 1) = (-40*sqrt(7)-140)/(560+sqrt(7)), (2, 2) = 0, (2, 3) = (280-32*sqrt(7))/(560+sqrt(7)), (3, 1) = (-80*sqrt(7)-35)/(560+sqrt(7)), (3, 2) = (-280+32*sqrt(7))/(560+sqrt(7)), (3, 3) = 0})

Matrix(%id = 36893490078408578100)

(1)

mtest := simplify(M+M^%T)

Matrix(%id = 36893490078408571348)

(2)

LinearAlgebra:-ZeroMatrix(3)

Matrix(%id = 36893490078408566412)

(3)

is(mtest = LinearAlgebra:-ZeroMatrix(3))

false

(4)

NULL

Download 2025-05-30_is_Matrix_skew-symmetric.mw

I used Maple’s odetest to check the validity of 36 exact solutions.

About half of them return zero, meaning they satisfy the ODE correctly. But the other half don’t — odetest gives nonzero expressions.

My question is:

Could there be a mistake in my assumptions, or are some of these solutions only valid under specific conditions?

I’d appreciate any clarification or suggestions.

ode-test-36.mw

Hello!

I use Maple to calculate a variety of physiology questions. But i keeps using the standardized SI unites and not the ones i plug in. Is there a way to get maple to behave differently? Ive added a screenshot of an example. It comes out in m3/s when i just want it in ml/min. 

GFR = (18.2*Unit(('mg')/('ml')))*1.5*Unit(('ml')/('min'))/(0.201*Unit(('mg')/('ml')));
 = 
                                            / 3\
                                            |m |
                GFR = 0.000002263681592 Unit|--|
                                            \s /

I'm looking for a flatten procedure for matrices (without first having to convert the matrix to a list, flatten it, and finally convert it back).
In this example, I am trying to generalize the matrix R to higher dimensions (here a 3 by 3 matrix, denoted as A, is used). I'm using a function, denoted as g, to construct a matrix. Obviously, the function applies to each cell and therefore, each cell contains a matrix in the resulting matrix. A flatten command would solve the problem. As a work-around I reconstruct the matrix In this example, but that is hard to generalize to more dimensions (or not?)

restart; kernelopts(version); interface(version); with(LinearAlgebra); with(combinat); interface(rtablesize = 16)

`Maple 2024.2, X86 64 WINDOWS, Oct 29 2024, Build ID 1872373`

 

`Standard Worksheet Interface, Maple 2024.2, Windows 11, October 29 2024 Build ID 1872373`

 

[10, 10]

(1)

Antidiagonal := proc (n) local Q, r, c; Q := Matrix(n, n); seq(seq(`if`(r+c = RowDimension(Q)+1, assign('Q[r, c]', 1), assign('Q[r, c]', 0)), r = 1 .. RowDimension(Q)), c = 1 .. ColumnDimension(Q)); return Q end proc

A := Matrix(3, 3, symbol = a)

R := `<,>`(`<|>`(Adjoint(A([2, 3], [2, 3])), -Adjoint(A([1, 3], [2, 3])), Adjoint(A([1, 2], [2, 3]))), `<|>`(-Adjoint(A([2, 3], [1, 3])), Adjoint(A([1, 3], [1, 3])), -Adjoint(A([1, 2], [1, 3]))), `<|>`(Adjoint(A([2, 3], [1, 2])), -Adjoint(A([1, 3], [1, 2])), Adjoint(A([1, 2], [1, 2]))))

Matrix(%id = 36893490582445267772)

(2)

U := choose(3, 2)

[[1, 2], [1, 3], [2, 3]]

(3)

g := proc (r, c) options operator, arrow; Adjoint((eval*A^%T)(U[c], U[r])) end proc

proc (r, c) options operator, arrow; LinearAlgebra:-Adjoint((eval(A^%T))(U[c], U[r])) end proc

(4)

Q := Matrix(3, g)

Matrix(%id = 36893490582395297788)

(5)

Q := Antidiagonal(3).Q.Antidiagonal(3)

Matrix(%id = 36893490582401641396)

(6)

U := `<,>`(`<|>`(Q[1, 1], Q[1, 2], Q[1, 3]), `<|>`(Q[2, 1], Q[2, 2], Q[2, 3]), `<|>`(Q[3, 1], Q[3, 2], Q[3, 3]))

Matrix(%id = 36893490582412939004)

(7)

R-Matrix(6, 6, [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]]).U^%T.Matrix(6, 6, [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]])

Matrix(%id = 36893490582417081876)

(8)


Download Flatten_a_matrix.mw

Hi everyone,

I've encountered something odd while working with Maple's pdetest function. When I manually evaluate my proposed solution using eval() followed by simplify(), I get the expected identity 0 = 0, which suggests the solution satisfies the PDE. However, when I test the same solution using pdetest, it doesn't return zero. This inconsistency has left me unsure whether my solution is actually valid or if I'm missing something.

Has anyone else experienced this kind of discrepancy? Could this be due to how pdetest handles derivatives or symbolic simplification internally?

Any insights or suggestions would be greatly appreciated!

Download pde-test.mw

Hi,

I try to creat an activity on Statistics, and I'm stuck on the bar chart, ( in the last part of my worksheet) with xi on the x-axis (Ox) and ni on the y-axis (Oy). I'm using the BarChart command, but it's not giving the expected result.

Ideas?

S4_Statistiques_Descriptives_AxeTravail_Complet.mw

Dear Power Users,

This is probably a simple question for you but I am stuck. In the attached worksheet I would like to plot (the plot is called P5) a vector with units (mm) against a vector without units. This didn't work out, so I removed the units from the vector with units, and this plotted but after the conversion the numeric values are no longer in mm but inches. How can I correct this?

Thank you in advance for your time and willingness to help.

testSheetHorseShoe.mw

in some of my function i have a big problem which i can't plot thus function even i know what is the shape of plot, i have two type of ploting directly giving parameter and using explor but for this kind of plot we can't use explor so i have to give the function directly parameter but is wasting my time a lot and i can't get my plot even spending a days by changing parameter one by one, my questions is this how i can plot this kind of function without bieng a singular i need this function to be non singular is not importan about the parameter can be any number 
thanks for any help 

plots-long_term_.mw

the shape of plot must be like this but must have two of them 

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